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<channel>
    <title>MongoDB Jira</title>
    <link>https://jira.mongodb.org</link>
    <description>This file is an XML representation of an issue</description>
    <language>en-us</language>    <build-info>
        <version>9.7.1</version>
        <build-number>970001</build-number>
        <build-date>13-04-2023</build-date>
    </build-info>


<item>
            <title>[SERVER-79622] [CQF] Improve intersectDNFIntervals behavior for variable bounds</title>
                <link>https://jira.mongodb.org/browse/SERVER-79622</link>
                <project id="10000" key="SERVER">Core Server</project>
                    <description>&lt;p&gt;&lt;a href=&quot;https://github.com/10gen/mongo/blob/3f6b4924e180de522e99ea700e474a379ba8152d/src/mongo/db/query/optimizer/utils/interval_utils.cpp#L603&quot; class=&quot;external-link&quot; target=&quot;_blank&quot; rel=&quot;nofollow noopener&quot;&gt;intersectDNFIntervals&lt;/a&gt; produces an overly complicated result for simple inputs:&lt;/p&gt;

&lt;p&gt;Input: &lt;/p&gt;
&lt;p/&gt;
&lt;div id=&quot;syntaxplugin&quot; class=&quot;syntaxplugin&quot; style=&quot;border: 1px dashed #bbb; border-radius: 5px !important; overflow: auto; max-height: 30em;&quot;&gt;
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					&lt;pre style=&quot;font-size: 1em; margin: 0 10px;   width: auto; padding: 0;&quot;&gt;&lt;span style=&quot;color: black; font-family: &apos;Consolas&apos;, &apos;Bitstream Vera Sans Mono&apos;, &apos;Courier New&apos;, Courier, monospace !important;&quot;&gt;    {&amp;lt;Const [&lt;/span&gt;&lt;span style=&quot;color: blue; font-family: &apos;Consolas&apos;, &apos;Bitstream Vera Sans Mono&apos;, &apos;Courier New&apos;, Courier, monospace !important;&quot;&gt;&quot;&quot;&lt;/span&gt;&lt;span style=&quot;color: black; font-family: &apos;Consolas&apos;, &apos;Bitstream Vera Sans Mono&apos;, &apos;Courier New&apos;, Courier, monospace !important;&quot;&gt;]}&lt;/span&gt;&lt;/pre&gt;
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						&lt;td  style=&quot; line-height: 1.4em !important; padding: 0em; vertical-align: top;&quot;&gt;
					&lt;pre style=&quot;font-size: 1em; margin: 0 10px;   width: auto; padding: 0;&quot;&gt;&lt;span style=&quot;color: black; font-family: &apos;Consolas&apos;, &apos;Bitstream Vera Sans Mono&apos;, &apos;Courier New&apos;, Courier, monospace !important;&quot;&gt; ^ &lt;/span&gt;&lt;/pre&gt;
			&lt;/td&gt;
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				&lt;tr id=&quot;syntaxplugin_code_and_gutter&quot;&gt;
						&lt;td  style=&quot; line-height: 1.4em !important; padding: 0em; vertical-align: top;&quot;&gt;
					&lt;pre style=&quot;font-size: 1em; margin: 0 10px;   width: auto; padding: 0;&quot;&gt;&lt;span style=&quot;color: black; font-family: &apos;Consolas&apos;, &apos;Bitstream Vera Sans Mono&apos;, &apos;Courier New&apos;, Courier, monospace !important;&quot;&gt;    {&amp;gt;FunctionCall [getParam] Const [&lt;/span&gt;&lt;span style=&quot;color: #009900; font-family: &apos;Consolas&apos;, &apos;Bitstream Vera Sans Mono&apos;, &apos;Courier New&apos;, Courier, monospace !important;&quot;&gt;0&lt;/span&gt;&lt;span style=&quot;color: black; font-family: &apos;Consolas&apos;, &apos;Bitstream Vera Sans Mono&apos;, &apos;Courier New&apos;, Courier, monospace !important;&quot;&gt;]}&lt;/span&gt;&lt;/pre&gt;
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&lt;/div&gt;
&lt;p/&gt;

&lt;p&gt;Output:&lt;/p&gt;
&lt;p/&gt;
&lt;div id=&quot;syntaxplugin&quot; class=&quot;syntaxplugin&quot; style=&quot;border: 1px dashed #bbb; border-radius: 5px !important; overflow: auto; max-height: 30em;&quot;&gt;
&lt;table cellspacing=&quot;0&quot; cellpadding=&quot;0&quot; border=&quot;0&quot; width=&quot;100%&quot; style=&quot;font-size: 1em; line-height: 1.4em !important; font-weight: normal; font-style: normal; color: black;&quot;&gt;
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					&lt;pre style=&quot;font-size: 1em; margin: 0 10px;  margin-top: 10px;   width: auto; padding: 0;&quot;&gt;&lt;span style=&quot;color: black; font-family: &apos;Consolas&apos;, &apos;Bitstream Vera Sans Mono&apos;, &apos;Courier New&apos;, Courier, monospace !important;&quot;&gt;{&lt;/span&gt;&lt;/pre&gt;
			&lt;/td&gt;
		&lt;/tr&gt;
				&lt;tr id=&quot;syntaxplugin_code_and_gutter&quot;&gt;
						&lt;td  style=&quot; line-height: 1.4em !important; padding: 0em; vertical-align: top;&quot;&gt;
					&lt;pre style=&quot;font-size: 1em; margin: 0 10px;   width: auto; padding: 0;&quot;&gt;&lt;span style=&quot;color: black; font-family: &apos;Consolas&apos;, &apos;Bitstream Vera Sans Mono&apos;, &apos;Courier New&apos;, Courier, monospace !important;&quot;&gt;    {{[If [] BinaryOp [And] BinaryOp [And] BinaryOp [Or] BinaryOp [And] BinaryOp [Lt] FunctionCall [getParam] Const [&lt;/span&gt;&lt;span style=&quot;color: #009900; font-family: &apos;Consolas&apos;, &apos;Bitstream Vera Sans Mono&apos;, &apos;Courier New&apos;, Courier, monospace !important;&quot;&gt;0&lt;/span&gt;&lt;span style=&quot;color: black; font-family: &apos;Consolas&apos;, &apos;Bitstream Vera Sans Mono&apos;, &apos;Courier New&apos;, Courier, monospace !important;&quot;&gt;] Const [&lt;/span&gt;&lt;span style=&quot;color: blue; font-family: &apos;Consolas&apos;, &apos;Bitstream Vera Sans Mono&apos;, &apos;Courier New&apos;, Courier, monospace !important;&quot;&gt;&quot;&quot;&lt;/span&gt;&lt;span style=&quot;color: black; font-family: &apos;Consolas&apos;, &apos;Bitstream Vera Sans Mono&apos;, &apos;Courier New&apos;, Courier, monospace !important;&quot;&gt;] Const [&lt;/span&gt;&lt;span style=&quot;color: #006699; font-weight: bold; font-family: &apos;Consolas&apos;, &apos;Bitstream Vera Sans Mono&apos;, &apos;Courier New&apos;, Courier, monospace !important;&quot;&gt;true&lt;/span&gt;&lt;span style=&quot;color: black; font-family: &apos;Consolas&apos;, &apos;Bitstream Vera Sans Mono&apos;, &apos;Courier New&apos;, Courier, monospace !important;&quot;&gt;] BinaryOp [Or] BinaryOp [And] BinaryOp [Lt] Const [minKey] FunctionCall [getParam] Const [&lt;/span&gt;&lt;span style=&quot;color: #009900; font-family: &apos;Consolas&apos;, &apos;Bitstream Vera Sans Mono&apos;, &apos;Courier New&apos;, Courier, monospace !important;&quot;&gt;0&lt;/span&gt;&lt;span style=&quot;color: black; font-family: &apos;Consolas&apos;, &apos;Bitstream Vera Sans Mono&apos;, &apos;Courier New&apos;, Courier, monospace !important;&quot;&gt;] BinaryOp [Lt] FunctionCall [getParam] Const [&lt;/span&gt;&lt;span style=&quot;color: #009900; font-family: &apos;Consolas&apos;, &apos;Bitstream Vera Sans Mono&apos;, &apos;Courier New&apos;, Courier, monospace !important;&quot;&gt;0&lt;/span&gt;&lt;span style=&quot;color: black; font-family: &apos;Consolas&apos;, &apos;Bitstream Vera Sans Mono&apos;, &apos;Courier New&apos;, Courier, monospace !important;&quot;&gt;] Const [&lt;/span&gt;&lt;span style=&quot;color: blue; font-family: &apos;Consolas&apos;, &apos;Bitstream Vera Sans Mono&apos;, &apos;Courier New&apos;, Courier, monospace !important;&quot;&gt;&quot;&quot;&lt;/span&gt;&lt;span style=&quot;color: black; font-family: &apos;Consolas&apos;, &apos;Bitstream Vera Sans Mono&apos;, &apos;Courier New&apos;, Courier, monospace !important;&quot;&gt;] Const [&lt;/span&gt;&lt;span style=&quot;color: #006699; font-weight: bold; font-family: &apos;Consolas&apos;, &apos;Bitstream Vera Sans Mono&apos;, &apos;Courier New&apos;, Courier, monospace !important;&quot;&gt;false&lt;/span&gt;&lt;span style=&quot;color: black; font-family: &apos;Consolas&apos;, &apos;Bitstream Vera Sans Mono&apos;, &apos;Courier New&apos;, Courier, monospace !important;&quot;&gt;] BinaryOp [Lt] FunctionCall [getParam] Const [&lt;/span&gt;&lt;span style=&quot;color: #009900; font-family: &apos;Consolas&apos;, &apos;Bitstream Vera Sans Mono&apos;, &apos;Courier New&apos;, Courier, monospace !important;&quot;&gt;0&lt;/span&gt;&lt;span style=&quot;color: black; font-family: &apos;Consolas&apos;, &apos;Bitstream Vera Sans Mono&apos;, &apos;Courier New&apos;, Courier, monospace !important;&quot;&gt;] Const [maxKey] Const [&lt;/span&gt;&lt;span style=&quot;color: #006699; font-weight: bold; font-family: &apos;Consolas&apos;, &apos;Bitstream Vera Sans Mono&apos;, &apos;Courier New&apos;, Courier, monospace !important;&quot;&gt;false&lt;/span&gt;&lt;span style=&quot;color: black; font-family: &apos;Consolas&apos;, &apos;Bitstream Vera Sans Mono&apos;, &apos;Courier New&apos;, Courier, monospace !important;&quot;&gt;] Const [minKey] Const [maxKey], Const [minKey]]}}&lt;/span&gt;&lt;/pre&gt;
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					&lt;pre style=&quot;font-size: 1em; margin: 0 10px;   width: auto; padding: 0;&quot;&gt;&lt;span style=&quot;color: black; font-family: &apos;Consolas&apos;, &apos;Bitstream Vera Sans Mono&apos;, &apos;Courier New&apos;, Courier, monospace !important;&quot;&gt; U &lt;/span&gt;&lt;/pre&gt;
			&lt;/td&gt;
		&lt;/tr&gt;
				&lt;tr id=&quot;syntaxplugin_code_and_gutter&quot;&gt;
						&lt;td  style=&quot; line-height: 1.4em !important; padding: 0em; vertical-align: top;&quot;&gt;
					&lt;pre style=&quot;font-size: 1em; margin: 0 10px;   width: auto; padding: 0;&quot;&gt;&lt;span style=&quot;color: black; font-family: &apos;Consolas&apos;, &apos;Bitstream Vera Sans Mono&apos;, &apos;Courier New&apos;, Courier, monospace !important;&quot;&gt;    {{[Const [maxKey], If [] BinaryOp [And] BinaryOp [And] BinaryOp [Or] BinaryOp [And] BinaryOp [Lt] FunctionCall [getParam] Const [&lt;/span&gt;&lt;span style=&quot;color: #009900; font-family: &apos;Consolas&apos;, &apos;Bitstream Vera Sans Mono&apos;, &apos;Courier New&apos;, Courier, monospace !important;&quot;&gt;0&lt;/span&gt;&lt;span style=&quot;color: black; font-family: &apos;Consolas&apos;, &apos;Bitstream Vera Sans Mono&apos;, &apos;Courier New&apos;, Courier, monospace !important;&quot;&gt;] Const [&lt;/span&gt;&lt;span style=&quot;color: blue; font-family: &apos;Consolas&apos;, &apos;Bitstream Vera Sans Mono&apos;, &apos;Courier New&apos;, Courier, monospace !important;&quot;&gt;&quot;&quot;&lt;/span&gt;&lt;span style=&quot;color: black; font-family: &apos;Consolas&apos;, &apos;Bitstream Vera Sans Mono&apos;, &apos;Courier New&apos;, Courier, monospace !important;&quot;&gt;] Const [&lt;/span&gt;&lt;span style=&quot;color: #006699; font-weight: bold; font-family: &apos;Consolas&apos;, &apos;Bitstream Vera Sans Mono&apos;, &apos;Courier New&apos;, Courier, monospace !important;&quot;&gt;true&lt;/span&gt;&lt;span style=&quot;color: black; font-family: &apos;Consolas&apos;, &apos;Bitstream Vera Sans Mono&apos;, &apos;Courier New&apos;, Courier, monospace !important;&quot;&gt;] BinaryOp [Or] BinaryOp [And] BinaryOp [Lt] Const [minKey] FunctionCall [getParam] Const [&lt;/span&gt;&lt;span style=&quot;color: #009900; font-family: &apos;Consolas&apos;, &apos;Bitstream Vera Sans Mono&apos;, &apos;Courier New&apos;, Courier, monospace !important;&quot;&gt;0&lt;/span&gt;&lt;span style=&quot;color: black; font-family: &apos;Consolas&apos;, &apos;Bitstream Vera Sans Mono&apos;, &apos;Courier New&apos;, Courier, monospace !important;&quot;&gt;] BinaryOp [Lt] FunctionCall [getParam] Const [&lt;/span&gt;&lt;span style=&quot;color: #009900; font-family: &apos;Consolas&apos;, &apos;Bitstream Vera Sans Mono&apos;, &apos;Courier New&apos;, Courier, monospace !important;&quot;&gt;0&lt;/span&gt;&lt;span style=&quot;color: black; font-family: &apos;Consolas&apos;, &apos;Bitstream Vera Sans Mono&apos;, &apos;Courier New&apos;, Courier, monospace !important;&quot;&gt;] Const [&lt;/span&gt;&lt;span style=&quot;color: blue; font-family: &apos;Consolas&apos;, &apos;Bitstream Vera Sans Mono&apos;, &apos;Courier New&apos;, Courier, monospace !important;&quot;&gt;&quot;&quot;&lt;/span&gt;&lt;span style=&quot;color: black; font-family: &apos;Consolas&apos;, &apos;Bitstream Vera Sans Mono&apos;, &apos;Courier New&apos;, Courier, monospace !important;&quot;&gt;] Const [&lt;/span&gt;&lt;span style=&quot;color: #006699; font-weight: bold; font-family: &apos;Consolas&apos;, &apos;Bitstream Vera Sans Mono&apos;, &apos;Courier New&apos;, Courier, monospace !important;&quot;&gt;false&lt;/span&gt;&lt;span style=&quot;color: black; font-family: &apos;Consolas&apos;, &apos;Bitstream Vera Sans Mono&apos;, &apos;Courier New&apos;, Courier, monospace !important;&quot;&gt;] BinaryOp [Lt] FunctionCall [getParam] Const [&lt;/span&gt;&lt;span style=&quot;color: #009900; font-family: &apos;Consolas&apos;, &apos;Bitstream Vera Sans Mono&apos;, &apos;Courier New&apos;, Courier, monospace !important;&quot;&gt;0&lt;/span&gt;&lt;span style=&quot;color: black; font-family: &apos;Consolas&apos;, &apos;Bitstream Vera Sans Mono&apos;, &apos;Courier New&apos;, Courier, monospace !important;&quot;&gt;] Const [maxKey] Const [&lt;/span&gt;&lt;span style=&quot;color: #006699; font-weight: bold; font-family: &apos;Consolas&apos;, &apos;Bitstream Vera Sans Mono&apos;, &apos;Courier New&apos;, Courier, monospace !important;&quot;&gt;false&lt;/span&gt;&lt;span style=&quot;color: black; font-family: &apos;Consolas&apos;, &apos;Bitstream Vera Sans Mono&apos;, &apos;Courier New&apos;, Courier, monospace !important;&quot;&gt;] Const [maxKey] Const [minKey]]}}&lt;/span&gt;&lt;/pre&gt;
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					&lt;pre style=&quot;font-size: 1em; margin: 0 10px;   width: auto; padding: 0;&quot;&gt;&lt;span style=&quot;color: black; font-family: &apos;Consolas&apos;, &apos;Bitstream Vera Sans Mono&apos;, &apos;Courier New&apos;, Courier, monospace !important;&quot;&gt; U &lt;/span&gt;&lt;/pre&gt;
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		&lt;/tr&gt;
				&lt;tr id=&quot;syntaxplugin_code_and_gutter&quot;&gt;
						&lt;td  style=&quot; line-height: 1.4em !important; padding: 0em; vertical-align: top;&quot;&gt;
					&lt;pre style=&quot;font-size: 1em; margin: 0 10px;   width: auto; padding: 0;&quot;&gt;&lt;span style=&quot;color: black; font-family: &apos;Consolas&apos;, &apos;Bitstream Vera Sans Mono&apos;, &apos;Courier New&apos;, Courier, monospace !important;&quot;&gt;    {{(If [] BinaryOp [Gte] Const [minKey] FunctionCall [getParam] Const [&lt;/span&gt;&lt;span style=&quot;color: #009900; font-family: &apos;Consolas&apos;, &apos;Bitstream Vera Sans Mono&apos;, &apos;Courier New&apos;, Courier, monospace !important;&quot;&gt;0&lt;/span&gt;&lt;span style=&quot;color: black; font-family: &apos;Consolas&apos;, &apos;Bitstream Vera Sans Mono&apos;, &apos;Courier New&apos;, Courier, monospace !important;&quot;&gt;] Const [minKey] FunctionCall [getParam] Const [&lt;/span&gt;&lt;span style=&quot;color: #009900; font-family: &apos;Consolas&apos;, &apos;Bitstream Vera Sans Mono&apos;, &apos;Courier New&apos;, Courier, monospace !important;&quot;&gt;0&lt;/span&gt;&lt;span style=&quot;color: black; font-family: &apos;Consolas&apos;, &apos;Bitstream Vera Sans Mono&apos;, &apos;Courier New&apos;, Courier, monospace !important;&quot;&gt;], Const [&lt;/span&gt;&lt;span style=&quot;color: blue; font-family: &apos;Consolas&apos;, &apos;Bitstream Vera Sans Mono&apos;, &apos;Courier New&apos;, Courier, monospace !important;&quot;&gt;&quot;&quot;&lt;/span&gt;&lt;span style=&quot;color: black; font-family: &apos;Consolas&apos;, &apos;Bitstream Vera Sans Mono&apos;, &apos;Courier New&apos;, Courier, monospace !important;&quot;&gt;])}}&lt;/span&gt;&lt;/pre&gt;
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						&lt;td  style=&quot; line-height: 1.4em !important; padding: 0em; vertical-align: top;&quot;&gt;
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&lt;/table&gt;
&lt;/div&gt;
&lt;p/&gt;

&lt;p&gt;The optimal result from this function would be a single interval, (getParam(0), &quot;&quot;). intersectDNFIntervals likely does not have special cases for intervals where the low bound is MinKey or the high bound is MaxKey.&lt;/p&gt;

&lt;p&gt;The number of intervals unioned in the result approximately doubles for each additional variable interval. We get 6 intervals with 3 variable intervals, 14 intervals for 4 variable intervals, etc. This is likely because the function &lt;a href=&quot;https://github.com/10gen/mongo/blob/3f6b4924e180de522e99ea700e474a379ba8152d/src/mongo/db/query/optimizer/utils/interval_utils.cpp#L625&quot; class=&quot;external-link&quot; target=&quot;_blank&quot; rel=&quot;nofollow noopener&quot;&gt;intersects two intervals at a time&lt;/a&gt; rather than analyzing the intervals all at once for a better result.&lt;/p&gt;

&lt;p&gt;This is relevant for parameterization of match expressions for the plan cache.&lt;/p&gt;

</description>
                <environment></environment>
        <key id="2407275">SERVER-79622</key>
            <summary>[CQF] Improve intersectDNFIntervals behavior for variable bounds</summary>
                <type id="4" iconUrl="https://jira.mongodb.org/secure/viewavatar?size=xsmall&amp;avatarId=14710&amp;avatarType=issuetype">Improvement</type>
                                            <priority id="3" iconUrl="https://jira.mongodb.org/images/icons/priorities/major.svg">Major - P3</priority>
                        <status id="1" iconUrl="https://jira.mongodb.org/images/icons/statuses/open.png" description="">Open</status>
                    <statusCategory id="2" key="new" colorName="default"/>
                                    <resolution id="-1">Unresolved</resolution>
                                        <assignee username="backlog-query-optimization">Backlog - Query Optimization</assignee>
                                    <reporter username="matt.boros@mongodb.com">Matt Boros</reporter>
                        <labels>
                    </labels>
                <created>Wed, 2 Aug 2023 16:29:55 +0000</created>
                <updated>Tue, 6 Feb 2024 16:33:12 +0000</updated>
                                                                                                <votes>0</votes>
                                    <watches>6</watches>
                                                                                                                <comments>
                            <comment id="5608652" author="david.percy" created="Wed, 2 Aug 2023 19:53:53 +0000"  >&lt;p&gt;To apply this idea to the example in this ticket: we&apos;re starting with this conjunction:&lt;/p&gt;
&lt;p/&gt;
&lt;div id=&quot;syntaxplugin&quot; class=&quot;syntaxplugin&quot; style=&quot;border: 1px dashed #bbb; border-radius: 5px !important; overflow: auto; max-height: 30em;&quot;&gt;
&lt;table cellspacing=&quot;0&quot; cellpadding=&quot;0&quot; border=&quot;0&quot; width=&quot;100%&quot; style=&quot;font-size: 1em; line-height: 1.4em !important; font-weight: normal; font-style: normal; color: black;&quot;&gt;
		&lt;tbody &gt;
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						&lt;td  style=&quot; line-height: 1.4em !important; padding: 0em; vertical-align: top;&quot;&gt;
					&lt;pre style=&quot;font-size: 1em; margin: 0 10px;  margin-top: 10px;   margin-bottom: 10px;  width: auto; padding: 0;&quot;&gt;&lt;span style=&quot;color: black; font-family: &apos;Consolas&apos;, &apos;Bitstream Vera Sans Mono&apos;, &apos;Courier New&apos;, Courier, monospace !important;&quot;&gt;[minKey, &lt;/span&gt;&lt;span style=&quot;color: blue; font-family: &apos;Consolas&apos;, &apos;Bitstream Vera Sans Mono&apos;, &apos;Courier New&apos;, Courier, monospace !important;&quot;&gt;&quot;&quot;&lt;/span&gt;&lt;span style=&quot;color: black; font-family: &apos;Consolas&apos;, &apos;Bitstream Vera Sans Mono&apos;, &apos;Courier New&apos;, Courier, monospace !important;&quot;&gt;) ^ (param0, maxKey]&lt;/span&gt;&lt;/pre&gt;
			&lt;/td&gt;
		&lt;/tr&gt;
			&lt;/tbody&gt;
&lt;/table&gt;
&lt;/div&gt;
&lt;p/&gt;
&lt;p&gt;With half-intervals it would be represented this way instead:&lt;/p&gt;
&lt;p/&gt;
&lt;div id=&quot;syntaxplugin&quot; class=&quot;syntaxplugin&quot; style=&quot;border: 1px dashed #bbb; border-radius: 5px !important; overflow: auto; max-height: 30em;&quot;&gt;
&lt;table cellspacing=&quot;0&quot; cellpadding=&quot;0&quot; border=&quot;0&quot; width=&quot;100%&quot; style=&quot;font-size: 1em; line-height: 1.4em !important; font-weight: normal; font-style: normal; color: black;&quot;&gt;
		&lt;tbody &gt;
				&lt;tr id=&quot;syntaxplugin_code_and_gutter&quot;&gt;
						&lt;td  style=&quot; line-height: 1.4em !important; padding: 0em; vertical-align: top;&quot;&gt;
					&lt;pre style=&quot;font-size: 1em; margin: 0 10px;  margin-top: 10px;   margin-bottom: 10px;  width: auto; padding: 0;&quot;&gt;&lt;span style=&quot;color: black; font-family: &apos;Consolas&apos;, &apos;Bitstream Vera Sans Mono&apos;, &apos;Courier New&apos;, Courier, monospace !important;&quot;&gt;[minKey  ^  &lt;/span&gt;&lt;span style=&quot;color: blue; font-family: &apos;Consolas&apos;, &apos;Bitstream Vera Sans Mono&apos;, &apos;Courier New&apos;, Courier, monospace !important;&quot;&gt;&quot;&quot;&lt;/span&gt;&lt;span style=&quot;color: black; font-family: &apos;Consolas&apos;, &apos;Bitstream Vera Sans Mono&apos;, &apos;Courier New&apos;, Courier, monospace !important;&quot;&gt;)  ^  (param0  ^  maxKey] &lt;/span&gt;&lt;/pre&gt;
			&lt;/td&gt;
		&lt;/tr&gt;
			&lt;/tbody&gt;
&lt;/table&gt;
&lt;/div&gt;
&lt;p/&gt;
&lt;p&gt;But &lt;tt&gt;&lt;span class=&quot;error&quot;&gt;&amp;#91;minKey and maxKey&amp;#93;&lt;/span&gt;&lt;/tt&gt; are both trivially-true, so we&apos;d drop them:&lt;/p&gt;
&lt;p/&gt;
&lt;div id=&quot;syntaxplugin&quot; class=&quot;syntaxplugin&quot; style=&quot;border: 1px dashed #bbb; border-radius: 5px !important; overflow: auto; max-height: 30em;&quot;&gt;
&lt;table cellspacing=&quot;0&quot; cellpadding=&quot;0&quot; border=&quot;0&quot; width=&quot;100%&quot; style=&quot;font-size: 1em; line-height: 1.4em !important; font-weight: normal; font-style: normal; color: black;&quot;&gt;
		&lt;tbody &gt;
				&lt;tr id=&quot;syntaxplugin_code_and_gutter&quot;&gt;
						&lt;td  style=&quot; line-height: 1.4em !important; padding: 0em; vertical-align: top;&quot;&gt;
					&lt;pre style=&quot;font-size: 1em; margin: 0 10px;  margin-top: 10px;   margin-bottom: 10px;  width: auto; padding: 0;&quot;&gt;&lt;span style=&quot;color: blue; font-family: &apos;Consolas&apos;, &apos;Bitstream Vera Sans Mono&apos;, &apos;Courier New&apos;, Courier, monospace !important;&quot;&gt;&quot;&quot;&lt;/span&gt;&lt;span style=&quot;color: black; font-family: &apos;Consolas&apos;, &apos;Bitstream Vera Sans Mono&apos;, &apos;Courier New&apos;, Courier, monospace !important;&quot;&gt;) ^ (param0&lt;/span&gt;&lt;/pre&gt;
			&lt;/td&gt;
		&lt;/tr&gt;
			&lt;/tbody&gt;
&lt;/table&gt;
&lt;/div&gt;
&lt;p/&gt;
&lt;p&gt;And optionally rearrange:&lt;/p&gt;
&lt;p/&gt;
&lt;div id=&quot;syntaxplugin&quot; class=&quot;syntaxplugin&quot; style=&quot;border: 1px dashed #bbb; border-radius: 5px !important; overflow: auto; max-height: 30em;&quot;&gt;
&lt;table cellspacing=&quot;0&quot; cellpadding=&quot;0&quot; border=&quot;0&quot; width=&quot;100%&quot; style=&quot;font-size: 1em; line-height: 1.4em !important; font-weight: normal; font-style: normal; color: black;&quot;&gt;
		&lt;tbody &gt;
				&lt;tr id=&quot;syntaxplugin_code_and_gutter&quot;&gt;
						&lt;td  style=&quot; line-height: 1.4em !important; padding: 0em; vertical-align: top;&quot;&gt;
					&lt;pre style=&quot;font-size: 1em; margin: 0 10px;  margin-top: 10px;   margin-bottom: 10px;  width: auto; padding: 0;&quot;&gt;&lt;span style=&quot;color: black; font-family: &apos;Consolas&apos;, &apos;Bitstream Vera Sans Mono&apos;, &apos;Courier New&apos;, Courier, monospace !important;&quot;&gt;(param0  ^  &lt;/span&gt;&lt;span style=&quot;color: blue; font-family: &apos;Consolas&apos;, &apos;Bitstream Vera Sans Mono&apos;, &apos;Courier New&apos;, Courier, monospace !important;&quot;&gt;&quot;&quot;&lt;/span&gt;&lt;span style=&quot;color: black; font-family: &apos;Consolas&apos;, &apos;Bitstream Vera Sans Mono&apos;, &apos;Courier New&apos;, Courier, monospace !important;&quot;&gt;)&lt;/span&gt;&lt;/pre&gt;
			&lt;/td&gt;
		&lt;/tr&gt;
			&lt;/tbody&gt;
&lt;/table&gt;
&lt;/div&gt;
&lt;p/&gt;</comment>
                            <comment id="5608635" author="david.percy" created="Wed, 2 Aug 2023 19:45:19 +0000"  >&lt;p&gt;One thing I&apos;ve been wondering is whether it would be simpler to deal with half-intervals. An interval is a conjunction of two half-intervals, and we already have a DNF. A half-interval has only one endpoint, so there are fewer cases to consider. We wouldn&apos;t need auxiliary intervals.&lt;/p&gt;

&lt;p&gt;For example, take this intersection of 4 intervals:&lt;/p&gt;
&lt;p/&gt;
&lt;div id=&quot;syntaxplugin&quot; class=&quot;syntaxplugin&quot; style=&quot;border: 1px dashed #bbb; border-radius: 5px !important; overflow: auto; max-height: 30em;&quot;&gt;
&lt;table cellspacing=&quot;0&quot; cellpadding=&quot;0&quot; border=&quot;0&quot; width=&quot;100%&quot; style=&quot;font-size: 1em; line-height: 1.4em !important; font-weight: normal; font-style: normal; color: black;&quot;&gt;
		&lt;tbody &gt;
				&lt;tr id=&quot;syntaxplugin_code_and_gutter&quot;&gt;
						&lt;td  style=&quot; line-height: 1.4em !important; padding: 0em; vertical-align: top;&quot;&gt;
					&lt;pre style=&quot;font-size: 1em; margin: 0 10px;  margin-top: 10px;   margin-bottom: 10px;  width: auto; padding: 0;&quot;&gt;&lt;span style=&quot;color: black; font-family: &apos;Consolas&apos;, &apos;Bitstream Vera Sans Mono&apos;, &apos;Courier New&apos;, Courier, monospace !important;&quot;&gt;[lo1, hi1] ^ (lo2, hi2) ^ (lo3, hi3] ^ [lo4, hi4)&lt;/span&gt;&lt;/pre&gt;
			&lt;/td&gt;
		&lt;/tr&gt;
			&lt;/tbody&gt;
&lt;/table&gt;
&lt;/div&gt;
&lt;p/&gt;
&lt;p&gt;There are many combinations of inclusive/exclusive bounds to consider.&lt;/p&gt;

&lt;p&gt;Now instead think of it as a conjunction of 8 half-intervals:&lt;/p&gt;
&lt;p/&gt;
&lt;div id=&quot;syntaxplugin&quot; class=&quot;syntaxplugin&quot; style=&quot;border: 1px dashed #bbb; border-radius: 5px !important; overflow: auto; max-height: 30em;&quot;&gt;
&lt;table cellspacing=&quot;0&quot; cellpadding=&quot;0&quot; border=&quot;0&quot; width=&quot;100%&quot; style=&quot;font-size: 1em; line-height: 1.4em !important; font-weight: normal; font-style: normal; color: black;&quot;&gt;
		&lt;tbody &gt;
				&lt;tr id=&quot;syntaxplugin_code_and_gutter&quot;&gt;
						&lt;td  style=&quot; line-height: 1.4em !important; padding: 0em; vertical-align: top;&quot;&gt;
					&lt;pre style=&quot;font-size: 1em; margin: 0 10px;  margin-top: 10px;   margin-bottom: 10px;  width: auto; padding: 0;&quot;&gt;&lt;span style=&quot;color: black; font-family: &apos;Consolas&apos;, &apos;Bitstream Vera Sans Mono&apos;, &apos;Courier New&apos;, Courier, monospace !important;&quot;&gt;[lo1  ^  hi1]  ^  (lo2  ^  hi2)  ^  (lo3  ^  hi3]  ^  [lo4  ^  hi4)&lt;/span&gt;&lt;/pre&gt;
			&lt;/td&gt;
		&lt;/tr&gt;
			&lt;/tbody&gt;
&lt;/table&gt;
&lt;/div&gt;
&lt;p/&gt;
&lt;p&gt;This lets you rearrange them:&lt;/p&gt;
&lt;p/&gt;
&lt;div id=&quot;syntaxplugin&quot; class=&quot;syntaxplugin&quot; style=&quot;border: 1px dashed #bbb; border-radius: 5px !important; overflow: auto; max-height: 30em;&quot;&gt;
&lt;table cellspacing=&quot;0&quot; cellpadding=&quot;0&quot; border=&quot;0&quot; width=&quot;100%&quot; style=&quot;font-size: 1em; line-height: 1.4em !important; font-weight: normal; font-style: normal; color: black;&quot;&gt;
		&lt;tbody &gt;
				&lt;tr id=&quot;syntaxplugin_code_and_gutter&quot;&gt;
						&lt;td  style=&quot; line-height: 1.4em !important; padding: 0em; vertical-align: top;&quot;&gt;
					&lt;pre style=&quot;font-size: 1em; margin: 0 10px;  margin-top: 10px;   width: auto; padding: 0;&quot;&gt;&lt;span style=&quot;color: black; font-family: &apos;Consolas&apos;, &apos;Bitstream Vera Sans Mono&apos;, &apos;Courier New&apos;, Courier, monospace !important;&quot;&gt;// all the lower bounds together&lt;/span&gt;&lt;/pre&gt;
			&lt;/td&gt;
		&lt;/tr&gt;
				&lt;tr id=&quot;syntaxplugin_code_and_gutter&quot;&gt;
						&lt;td  style=&quot; line-height: 1.4em !important; padding: 0em; vertical-align: top;&quot;&gt;
					&lt;pre style=&quot;font-size: 1em; margin: 0 10px;   width: auto; padding: 0;&quot;&gt;&lt;span style=&quot;color: black; font-family: &apos;Consolas&apos;, &apos;Bitstream Vera Sans Mono&apos;, &apos;Courier New&apos;, Courier, monospace !important;&quot;&gt;[lo1  ^  [lo4  ^  (lo2  ^  (lo3 &lt;/span&gt;&lt;/pre&gt;
			&lt;/td&gt;
		&lt;/tr&gt;
				&lt;tr id=&quot;syntaxplugin_code_and_gutter&quot;&gt;
						&lt;td  style=&quot; line-height: 1.4em !important; padding: 0em; vertical-align: top;&quot;&gt;
					&lt;pre style=&quot;font-size: 1em; margin: 0 10px;   width: auto; padding: 0;&quot;&gt;&lt;span style=&quot;color: black; font-family: &apos;Consolas&apos;, &apos;Bitstream Vera Sans Mono&apos;, &apos;Courier New&apos;, Courier, monospace !important;&quot;&gt;^&lt;/span&gt;&lt;/pre&gt;
			&lt;/td&gt;
		&lt;/tr&gt;
				&lt;tr id=&quot;syntaxplugin_code_and_gutter&quot;&gt;
						&lt;td  style=&quot; line-height: 1.4em !important; padding: 0em; vertical-align: top;&quot;&gt;
					&lt;pre style=&quot;font-size: 1em; margin: 0 10px;   width: auto; padding: 0;&quot;&gt;&lt;span style=&quot;color: black; font-family: &apos;Consolas&apos;, &apos;Bitstream Vera Sans Mono&apos;, &apos;Courier New&apos;, Courier, monospace !important;&quot;&gt;// all the upper bounds together&lt;/span&gt;&lt;/pre&gt;
			&lt;/td&gt;
		&lt;/tr&gt;
				&lt;tr id=&quot;syntaxplugin_code_and_gutter&quot;&gt;
						&lt;td  style=&quot; line-height: 1.4em !important; padding: 0em; vertical-align: top;&quot;&gt;
					&lt;pre style=&quot;font-size: 1em; margin: 0 10px;   margin-bottom: 10px;  width: auto; padding: 0;&quot;&gt;&lt;span style=&quot;color: black; font-family: &apos;Consolas&apos;, &apos;Bitstream Vera Sans Mono&apos;, &apos;Courier New&apos;, Courier, monospace !important;&quot;&gt;hi1]  ^  hi3]  ^  hi2)  ^  hi4)&lt;/span&gt;&lt;/pre&gt;
			&lt;/td&gt;
		&lt;/tr&gt;
			&lt;/tbody&gt;
&lt;/table&gt;
&lt;/div&gt;
&lt;p/&gt;
&lt;p&gt;And then it&apos;s easy to combine half-intervals with the same inclusivity:&lt;/p&gt;
&lt;p/&gt;
&lt;div id=&quot;syntaxplugin&quot; class=&quot;syntaxplugin&quot; style=&quot;border: 1px dashed #bbb; border-radius: 5px !important; overflow: auto; max-height: 30em;&quot;&gt;
&lt;table cellspacing=&quot;0&quot; cellpadding=&quot;0&quot; border=&quot;0&quot; width=&quot;100%&quot; style=&quot;font-size: 1em; line-height: 1.4em !important; font-weight: normal; font-style: normal; color: black;&quot;&gt;
		&lt;tbody &gt;
				&lt;tr id=&quot;syntaxplugin_code_and_gutter&quot;&gt;
						&lt;td  style=&quot; line-height: 1.4em !important; padding: 0em; vertical-align: top;&quot;&gt;
					&lt;pre style=&quot;font-size: 1em; margin: 0 10px;  margin-top: 10px;   width: auto; padding: 0;&quot;&gt;&lt;span style=&quot;color: black; font-family: &apos;Consolas&apos;, &apos;Bitstream Vera Sans Mono&apos;, &apos;Courier New&apos;, Courier, monospace !important;&quot;&gt;[max(lo1,lo4) ^ (max(lo2,lo3)&lt;/span&gt;&lt;/pre&gt;
			&lt;/td&gt;
		&lt;/tr&gt;
				&lt;tr id=&quot;syntaxplugin_code_and_gutter&quot;&gt;
						&lt;td  style=&quot; line-height: 1.4em !important; padding: 0em; vertical-align: top;&quot;&gt;
					&lt;pre style=&quot;font-size: 1em; margin: 0 10px;   width: auto; padding: 0;&quot;&gt;&lt;span style=&quot;color: black; font-family: &apos;Consolas&apos;, &apos;Bitstream Vera Sans Mono&apos;, &apos;Courier New&apos;, Courier, monospace !important;&quot;&gt;^&lt;/span&gt;&lt;/pre&gt;
			&lt;/td&gt;
		&lt;/tr&gt;
				&lt;tr id=&quot;syntaxplugin_code_and_gutter&quot;&gt;
						&lt;td  style=&quot; line-height: 1.4em !important; padding: 0em; vertical-align: top;&quot;&gt;
					&lt;pre style=&quot;font-size: 1em; margin: 0 10px;   margin-bottom: 10px;  width: auto; padding: 0;&quot;&gt;&lt;span style=&quot;color: black; font-family: &apos;Consolas&apos;, &apos;Bitstream Vera Sans Mono&apos;, &apos;Courier New&apos;, Courier, monospace !important;&quot;&gt;min(hi1,hi3)]  ^  min(hi2,hi4))&lt;/span&gt;&lt;/pre&gt;
			&lt;/td&gt;
		&lt;/tr&gt;
			&lt;/tbody&gt;
&lt;/table&gt;
&lt;/div&gt;
&lt;p/&gt;
&lt;p&gt;Any conjunction of intervals can be normalized this way:&lt;/p&gt;
&lt;p/&gt;
&lt;div id=&quot;syntaxplugin&quot; class=&quot;syntaxplugin&quot; style=&quot;border: 1px dashed #bbb; border-radius: 5px !important; overflow: auto; max-height: 30em;&quot;&gt;
&lt;table cellspacing=&quot;0&quot; cellpadding=&quot;0&quot; border=&quot;0&quot; width=&quot;100%&quot; style=&quot;font-size: 1em; line-height: 1.4em !important; font-weight: normal; font-style: normal; color: black;&quot;&gt;
		&lt;tbody &gt;
				&lt;tr id=&quot;syntaxplugin_code_and_gutter&quot;&gt;
						&lt;td  style=&quot; line-height: 1.4em !important; padding: 0em; vertical-align: top;&quot;&gt;
					&lt;pre style=&quot;font-size: 1em; margin: 0 10px;  margin-top: 10px;   width: auto; padding: 0;&quot;&gt;&lt;span style=&quot;color: black; font-family: &apos;Consolas&apos;, &apos;Bitstream Vera Sans Mono&apos;, &apos;Courier New&apos;, Courier, monospace !important;&quot;&gt;[a ^ (b&lt;/span&gt;&lt;/pre&gt;
			&lt;/td&gt;
		&lt;/tr&gt;
				&lt;tr id=&quot;syntaxplugin_code_and_gutter&quot;&gt;
						&lt;td  style=&quot; line-height: 1.4em !important; padding: 0em; vertical-align: top;&quot;&gt;
					&lt;pre style=&quot;font-size: 1em; margin: 0 10px;   width: auto; padding: 0;&quot;&gt;&lt;span style=&quot;color: black; font-family: &apos;Consolas&apos;, &apos;Bitstream Vera Sans Mono&apos;, &apos;Courier New&apos;, Courier, monospace !important;&quot;&gt;^&lt;/span&gt;&lt;/pre&gt;
			&lt;/td&gt;
		&lt;/tr&gt;
				&lt;tr id=&quot;syntaxplugin_code_and_gutter&quot;&gt;
						&lt;td  style=&quot; line-height: 1.4em !important; padding: 0em; vertical-align: top;&quot;&gt;
					&lt;pre style=&quot;font-size: 1em; margin: 0 10px;   margin-bottom: 10px;  width: auto; padding: 0;&quot;&gt;&lt;span style=&quot;color: black; font-family: &apos;Consolas&apos;, &apos;Bitstream Vera Sans Mono&apos;, &apos;Courier New&apos;, Courier, monospace !important;&quot;&gt;c]  ^  d)&lt;/span&gt;&lt;/pre&gt;
			&lt;/td&gt;
		&lt;/tr&gt;
			&lt;/tbody&gt;
&lt;/table&gt;
&lt;/div&gt;
&lt;p/&gt;
&lt;p&gt;We don&apos;t need auxiliary intervals to represent the fact that the inclusivity depends on the values of a,b,c,d.&lt;/p&gt;

&lt;p&gt;When lowering to an expression, we would still have some conditionals comparing a,b and c,d:&lt;/p&gt;
&lt;p/&gt;
&lt;div id=&quot;syntaxplugin&quot; class=&quot;syntaxplugin&quot; style=&quot;border: 1px dashed #bbb; border-radius: 5px !important; overflow: auto; max-height: 30em;&quot;&gt;
&lt;table cellspacing=&quot;0&quot; cellpadding=&quot;0&quot; border=&quot;0&quot; width=&quot;100%&quot; style=&quot;font-size: 1em; line-height: 1.4em !important; font-weight: normal; font-style: normal; color: black;&quot;&gt;
		&lt;tbody &gt;
				&lt;tr id=&quot;syntaxplugin_code_and_gutter&quot;&gt;
						&lt;td  style=&quot; line-height: 1.4em !important; padding: 0em; vertical-align: top;&quot;&gt;
					&lt;pre style=&quot;font-size: 1em; margin: 0 10px;  margin-top: 10px;   width: auto; padding: 0;&quot;&gt;&lt;span style=&quot;color: black; font-family: &apos;Consolas&apos;, &apos;Bitstream Vera Sans Mono&apos;, &apos;Courier New&apos;, Courier, monospace !important;&quot;&gt;(a &amp;gt; b) ? a &amp;lt;= x : b &amp;lt; x&lt;/span&gt;&lt;/pre&gt;
			&lt;/td&gt;
		&lt;/tr&gt;
				&lt;tr id=&quot;syntaxplugin_code_and_gutter&quot;&gt;
						&lt;td  style=&quot; line-height: 1.4em !important; padding: 0em; vertical-align: top;&quot;&gt;
					&lt;pre style=&quot;font-size: 1em; margin: 0 10px;   width: auto; padding: 0;&quot;&gt;&lt;span style=&quot;color: black; font-family: &apos;Consolas&apos;, &apos;Bitstream Vera Sans Mono&apos;, &apos;Courier New&apos;, Courier, monospace !important;&quot;&gt;&amp;amp;&amp;amp;&lt;/span&gt;&lt;/pre&gt;
			&lt;/td&gt;
		&lt;/tr&gt;
				&lt;tr id=&quot;syntaxplugin_code_and_gutter&quot;&gt;
						&lt;td  style=&quot; line-height: 1.4em !important; padding: 0em; vertical-align: top;&quot;&gt;
					&lt;pre style=&quot;font-size: 1em; margin: 0 10px;   margin-bottom: 10px;  width: auto; padding: 0;&quot;&gt;&lt;span style=&quot;color: black; font-family: &apos;Consolas&apos;, &apos;Bitstream Vera Sans Mono&apos;, &apos;Courier New&apos;, Courier, monospace !important;&quot;&gt;(d &amp;lt; c) ? x &amp;lt; d : x &amp;lt;= c&lt;/span&gt;&lt;/pre&gt;
			&lt;/td&gt;
		&lt;/tr&gt;
			&lt;/tbody&gt;
&lt;/table&gt;
&lt;/div&gt;
&lt;p/&gt;
&lt;p&gt;and these would be constant-folded once a,b,c,d are known.&lt;/p&gt;

&lt;p&gt;I&apos;m not sure how to convert these to compound intervals (where each endpoint is a tuple), but probably a similar conditional would work. Ultimately you want something like:&lt;/p&gt;
&lt;p/&gt;
&lt;div id=&quot;syntaxplugin&quot; class=&quot;syntaxplugin&quot; style=&quot;border: 1px dashed #bbb; border-radius: 5px !important; overflow: auto; max-height: 30em;&quot;&gt;
&lt;table cellspacing=&quot;0&quot; cellpadding=&quot;0&quot; border=&quot;0&quot; width=&quot;100%&quot; style=&quot;font-size: 1em; line-height: 1.4em !important; font-weight: normal; font-style: normal; color: black;&quot;&gt;
		&lt;tbody &gt;
				&lt;tr id=&quot;syntaxplugin_code_and_gutter&quot;&gt;
						&lt;td  style=&quot; line-height: 1.4em !important; padding: 0em; vertical-align: top;&quot;&gt;
					&lt;pre style=&quot;font-size: 1em; margin: 0 10px;  margin-top: 10px;   margin-bottom: 10px;  width: auto; padding: 0;&quot;&gt;&lt;span style=&quot;color: black; font-family: &apos;Consolas&apos;, &apos;Bitstream Vera Sans Mono&apos;, &apos;Courier New&apos;, Courier, monospace !important;&quot;&gt;ixscan lowbound=(condition1 ? ks1 : ks2) highbound=(condition2 ? ks3 : ks4)&lt;/span&gt;&lt;/pre&gt;
			&lt;/td&gt;
		&lt;/tr&gt;
			&lt;/tbody&gt;
&lt;/table&gt;
&lt;/div&gt;
&lt;p/&gt;</comment>
                    </comments>
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